Refined Model for Analysis of Plates on Elastic Foundations

Abstract

Practicing engineers continue to use the Winkler model for the analysis of beams and plates resting on elastic foundations in spite of the disclosure of inconsistencies in the use of the Winkler model by past researchers. In this paper, using variational principles, the model developed by Vlasov and Leont'ev is refined, and a numerical model using the finite difference method is introduced to solve a rectangular plate resting on a layered soil medium. Instead of the coefficient of subgrade reaction of the soil, the material properties of the soil are used in the analysis. The basic parameters required for the analysis are computed from the geometry and material properties of the soil and the structure. Some of the basic inconsistencies in the classical Winkler model are brought out in this paper. Results of some examples are presented.